When we look at the nerve ending at the top of the nasal passage, we see that they are the nerves that extend from the brain. (this is the only area in the body , that nerves from the brain are exposed, outside the skull) When we breathe in through the nose, We get are sense of smell from these nerve endings.
But, this also allow oxygen to get to the brain in a more immediate time, than coming from the lungs through the blood stream. This has alot to do with the slowing a regulating of the Alpha, beta & theta waves in the frontal lobes of the brain. (Increased clarity, enlightenment, etc...)
So breathing out through the nose, just releases Carbon Monoxide (SP ?) to these nerve endings.
the benifits of breathing in through the nose & out through the mouth is Enormous! (Increased oxygen, clarity of thought, etc...)
For more info. There is a book called "Zen meditation & Psychotherapy" By: Tomio Hirai, MD
It gives a great explanation of the benifits of breathing-meditation & its benifits on the brain & body.
If you get deep into Taoist meditation then the breathing can get pretty complicated. Various techniques according to the season, or your purpose in doing the excercises.
Normally, during Tai Chi practice, it is as posted before, in throught the nose, using the diaphram, out through the mouth. If your school emphasizes Chi flow then you might be told to close your mouth on the inhale, with the tongue touching the roof of the mouth. On the exhale, open the mouth slightly, and drop the tongue. Something about completing the Chi circuit.